Type of solution of quadratic depends on the value of Discriminant: b^2  4ac
Roots are evaluated by factoring the equation of
aX^2 + bx + c
a ( X  b/ 2a ) ^2  ( b^2  4ac)/ 4a^2
X_{1}_{ }, X_{2 } = b/2a ±√(b^2  4ac) /2a
if b^2  4ac > 0 , then quadratic has 2 real roos
a. b^2 4ac is a perfect square then the roots are rational
b . b^2  4ac not a perfect square, then the roots are irrational
if b^2  4ac< 0 , then quadratic has 2 complex roots.
Quadratic always has 2 roots.
The irrational and complex roots has to appear as conjugate pair for the coefficients of the quadratic
to be integers.
i.e.
X = a ± bi
X = a ± √b
3/31/2014

Parviz F.